Given are N positive integers A_1,...,A_N.
Consider positive integers B_1, ..., B_N that satisfy the following condition.
Condition: For any i, j such that $1 \leq i < j \leq N, A_i B_i = A_j B_j$ holds.
Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.
Since the answer can be enormous, print the sum modulo (10^9 +7).

-----Constraints-----
- $1 \leq N \leq 10^4$
- $1 \leq A_i \leq 10^6$
- All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_1 ... A_N

-----Output-----
Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

-----Sample Input-----
3
2 3 4

-----Sample Output-----
13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

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